Reducción de Dimensionalidad¶

Introducción¶

• Hasta el momento, hemos visto datasets pequeños, con pocas características (columnas).
• Datasets con un mayor número de columnas son muy comunes. Estos producen:
  • Entrenamientos más lentos
  • Dificultad para encontrar una buena solución
• Es en este contexto donde se plantea la reducción de dimensionalidad
• Reducción de dimensionalidad viene acompañada de pérdida de información (ej: jpeg)

Author: Christophe Mehay

Principal Components Analysis (PCA-Análisis de Componentes Principales)¶

• Una de las técnicas más populares para reducción de dimensionalidad
• Identifica el hiperplano más cercano a los datos, y luego proyecta los datos en él.
• PCA nos permite:
  • Poder visualizar datos con alta dimensionalidad que de otra forma no sería posible
  • Reducción de dimensionalidad para mejora en la velocidad de entrenamiento
• En PCA, es importante que los datos se encuentren en la misma escala (sino, se debe escalar)
• PCA identifica los ejes de mayor varianza (componentes principales)

Usando PCA para visualización¶

In [1]:

import matplotlib.pyplot as plt
from sklearn.datasets import load_breast_cancer
import pandas as pd

cancer_data = load_breast_cancer(as_frame=True) # Para obtener datos como dataframe
print(cancer_data.target_names) # 0 Maligno, 1 benigno

import matplotlib.pyplot as plt from sklearn.datasets import load_breast_cancer import pandas as pd cancer_data = load_breast_cancer(as_frame=True) # Para obtener datos como dataframe print(cancer_data.target_names) # 0 Maligno, 1 benigno

['malignant' 'benign']

In [2]:

cancer_data.frame.head()

cancer_data.frame.head()

Out[2]:

	mean radius	mean texture	mean perimeter	mean area	mean smoothness	mean compactness	mean concavity	mean concave points	mean symmetry	mean fractal dimension	...	worst texture	worst perimeter	worst area	worst smoothness	worst compactness	worst concavity	worst concave points	worst symmetry	worst fractal dimension	target
0	17.99	10.38	122.80	1001.0	0.11840	0.27760	0.3001	0.14710	0.2419	0.07871	...	17.33	184.60	2019.0	0.1622	0.6656	0.7119	0.2654	0.4601	0.11890	0
1	20.57	17.77	132.90	1326.0	0.08474	0.07864	0.0869	0.07017	0.1812	0.05667	...	23.41	158.80	1956.0	0.1238	0.1866	0.2416	0.1860	0.2750	0.08902	0
2	19.69	21.25	130.00	1203.0	0.10960	0.15990	0.1974	0.12790	0.2069	0.05999	...	25.53	152.50	1709.0	0.1444	0.4245	0.4504	0.2430	0.3613	0.08758	0
3	11.42	20.38	77.58	386.1	0.14250	0.28390	0.2414	0.10520	0.2597	0.09744	...	26.50	98.87	567.7	0.2098	0.8663	0.6869	0.2575	0.6638	0.17300	0
4	20.29	14.34	135.10	1297.0	0.10030	0.13280	0.1980	0.10430	0.1809	0.05883	...	16.67	152.20	1575.0	0.1374	0.2050	0.4000	0.1625	0.2364	0.07678	0

5 rows × 31 columns

In [3]:

len(cancer_data.feature_names)

len(cancer_data.feature_names)

Out[3]:

30

In [4]:

df = cancer_data.frame
print(df.info())
df.head()

df = cancer_data.frame print(df.info()) df.head()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 569 entries, 0 to 568
Data columns (total 31 columns):
 #   Column                   Non-Null Count  Dtype  
---  ------                   --------------  -----  
 0   mean radius              569 non-null    float64
 1   mean texture             569 non-null    float64
 2   mean perimeter           569 non-null    float64
 3   mean area                569 non-null    float64
 4   mean smoothness          569 non-null    float64
 5   mean compactness         569 non-null    float64
 6   mean concavity           569 non-null    float64
 7   mean concave points      569 non-null    float64
 8   mean symmetry            569 non-null    float64
 9   mean fractal dimension   569 non-null    float64
 10  radius error             569 non-null    float64
 11  texture error            569 non-null    float64
 12  perimeter error          569 non-null    float64
 13  area error               569 non-null    float64
 14  smoothness error         569 non-null    float64
 15  compactness error        569 non-null    float64
 16  concavity error          569 non-null    float64
 17  concave points error     569 non-null    float64
 18  symmetry error           569 non-null    float64
 19  fractal dimension error  569 non-null    float64
 20  worst radius             569 non-null    float64
 21  worst texture            569 non-null    float64
 22  worst perimeter          569 non-null    float64
 23  worst area               569 non-null    float64
 24  worst smoothness         569 non-null    float64
 25  worst compactness        569 non-null    float64
 26  worst concavity          569 non-null    float64
 27  worst concave points     569 non-null    float64
 28  worst symmetry           569 non-null    float64
 29  worst fractal dimension  569 non-null    float64
 30  target                   569 non-null    int64  
dtypes: float64(30), int64(1)
memory usage: 137.9 KB
None

Out[4]:

	mean radius	mean texture	mean perimeter	mean area	mean smoothness	mean compactness	mean concavity	mean concave points	mean symmetry	mean fractal dimension	...	worst texture	worst perimeter	worst area	worst smoothness	worst compactness	worst concavity	worst concave points	worst symmetry	worst fractal dimension	target
0	17.99	10.38	122.80	1001.0	0.11840	0.27760	0.3001	0.14710	0.2419	0.07871	...	17.33	184.60	2019.0	0.1622	0.6656	0.7119	0.2654	0.4601	0.11890	0
1	20.57	17.77	132.90	1326.0	0.08474	0.07864	0.0869	0.07017	0.1812	0.05667	...	23.41	158.80	1956.0	0.1238	0.1866	0.2416	0.1860	0.2750	0.08902	0
2	19.69	21.25	130.00	1203.0	0.10960	0.15990	0.1974	0.12790	0.2069	0.05999	...	25.53	152.50	1709.0	0.1444	0.4245	0.4504	0.2430	0.3613	0.08758	0
3	11.42	20.38	77.58	386.1	0.14250	0.28390	0.2414	0.10520	0.2597	0.09744	...	26.50	98.87	567.7	0.2098	0.8663	0.6869	0.2575	0.6638	0.17300	0
4	20.29	14.34	135.10	1297.0	0.10030	0.13280	0.1980	0.10430	0.1809	0.05883	...	16.67	152.20	1575.0	0.1374	0.2050	0.4000	0.1625	0.2364	0.07678	0

5 rows × 31 columns

In [5]:

df.hist(bins=20,figsize=(15,10))
plt.tight_layout()
plt.show()

df.hist(bins=20,figsize=(15,10)) plt.tight_layout() plt.show()

In [6]:

from sklearn.preprocessing import StandardScaler

X = cancer_data.data
y = cancer_data.target

scaler = StandardScaler()
X = pd.DataFrame(scaler.fit_transform(X), columns=cancer_data.feature_names)

from sklearn.preprocessing import StandardScaler X = cancer_data.data y = cancer_data.target scaler = StandardScaler() X = pd.DataFrame(scaler.fit_transform(X), columns=cancer_data.feature_names)

In [7]:

X.head()

X.head()

Out[7]:

	mean radius	mean texture	mean perimeter	mean area	mean smoothness	mean compactness	mean concavity	mean concave points	mean symmetry	mean fractal dimension	...	worst radius	worst texture	worst perimeter	worst area	worst smoothness	worst compactness	worst concavity	worst concave points	worst symmetry	worst fractal dimension
0	1.097064	-2.073335	1.269934	0.984375	1.568466	3.283515	2.652874	2.532475	2.217515	2.255747	...	1.886690	-1.359293	2.303601	2.001237	1.307686	2.616665	2.109526	2.296076	2.750622	1.937015
1	1.829821	-0.353632	1.685955	1.908708	-0.826962	-0.487072	-0.023846	0.548144	0.001392	-0.868652	...	1.805927	-0.369203	1.535126	1.890489	-0.375612	-0.430444	-0.146749	1.087084	-0.243890	0.281190
2	1.579888	0.456187	1.566503	1.558884	0.942210	1.052926	1.363478	2.037231	0.939685	-0.398008	...	1.511870	-0.023974	1.347475	1.456285	0.527407	1.082932	0.854974	1.955000	1.152255	0.201391
3	-0.768909	0.253732	-0.592687	-0.764464	3.283553	3.402909	1.915897	1.451707	2.867383	4.910919	...	-0.281464	0.133984	-0.249939	-0.550021	3.394275	3.893397	1.989588	2.175786	6.046041	4.935010
4	1.750297	-1.151816	1.776573	1.826229	0.280372	0.539340	1.371011	1.428493	-0.009560	-0.562450	...	1.298575	-1.466770	1.338539	1.220724	0.220556	-0.313395	0.613179	0.729259	-0.868353	-0.397100

5 rows × 30 columns

In [8]:

# Todos los gráficos entre pares de columnas!
colors = {0:'red', 1:'green'}
color_map = y.map(colors)
columns = X.columns.tolist()

i = 0 
for x in columns:
    columns.remove(x)
    for y in columns:
        print("Plotting ", x, " vs ", y)
        X.plot.scatter(x=x, y=y, c=color_map)
        i += 1
print("Número de gráficos: ", i)
plt.show()

# Todos los gráficos entre pares de columnas! colors = {0:'red', 1:'green'} color_map = y.map(colors) columns = X.columns.tolist() i = 0 for x in columns: columns.remove(x) for y in columns: print("Plotting ", x, " vs ", y) X.plot.scatter(x=x, y=y, c=color_map) i += 1 print("Número de gráficos: ", i) plt.show()

Plotting  mean radius  vs  mean texture
Plotting  mean radius  vs  mean perimeter
Plotting  mean radius  vs  mean area
Plotting  mean radius  vs  mean smoothness
Plotting  mean radius  vs  mean compactness
Plotting  mean radius  vs  mean concavity
Plotting  mean radius  vs  mean concave points
Plotting  mean radius  vs  mean symmetry
Plotting  mean radius  vs  mean fractal dimension
Plotting  mean radius  vs  radius error
Plotting  mean radius  vs  texture error
Plotting  mean radius  vs  perimeter error
Plotting  mean radius  vs  area error
Plotting  mean radius  vs  smoothness error
Plotting  mean radius  vs  compactness error
Plotting  mean radius  vs  concavity error
Plotting  mean radius  vs  concave points error
Plotting  mean radius  vs  symmetry error
Plotting  mean radius  vs  fractal dimension error
Plotting  mean radius  vs  worst radius
Plotting  mean radius  vs  worst texture

/home/polivares/anaconda3/envs/DataScience/lib/python3.8/site-packages/pandas/plotting/_matplotlib/core.py:345: RuntimeWarning: More than 20 figures have been opened. Figures created through the pyplot interface (`matplotlib.pyplot.figure`) are retained until explicitly closed and may consume too much memory. (To control this warning, see the rcParam `figure.max_open_warning`).
  fig = self.plt.figure(figsize=self.figsize)

Plotting  mean radius  vs  worst perimeter
Plotting  mean radius  vs  worst area
Plotting  mean radius  vs  worst smoothness
Plotting  mean radius  vs  worst compactness
Plotting  mean radius  vs  worst concavity
Plotting  mean radius  vs  worst concave points
Plotting  mean radius  vs  worst symmetry
Plotting  mean radius  vs  worst fractal dimension
Plotting  mean perimeter  vs  mean texture
Plotting  mean perimeter  vs  mean area
Plotting  mean perimeter  vs  mean smoothness
Plotting  mean perimeter  vs  mean compactness
Plotting  mean perimeter  vs  mean concavity
Plotting  mean perimeter  vs  mean concave points
Plotting  mean perimeter  vs  mean symmetry
Plotting  mean perimeter  vs  mean fractal dimension
Plotting  mean perimeter  vs  radius error
Plotting  mean perimeter  vs  texture error
Plotting  mean perimeter  vs  perimeter error
Plotting  mean perimeter  vs  area error
Plotting  mean perimeter  vs  smoothness error
Plotting  mean perimeter  vs  compactness error
Plotting  mean perimeter  vs  concavity error
Plotting  mean perimeter  vs  concave points error
Plotting  mean perimeter  vs  symmetry error
Plotting  mean perimeter  vs  fractal dimension error
Plotting  mean perimeter  vs  worst radius
Plotting  mean perimeter  vs  worst texture
Plotting  mean perimeter  vs  worst perimeter
Plotting  mean perimeter  vs  worst area
Plotting  mean perimeter  vs  worst smoothness
Plotting  mean perimeter  vs  worst compactness
Plotting  mean perimeter  vs  worst concavity
Plotting  mean perimeter  vs  worst concave points
Plotting  mean perimeter  vs  worst symmetry
Plotting  mean perimeter  vs  worst fractal dimension
Plotting  mean smoothness  vs  mean texture
Plotting  mean smoothness  vs  mean area
Plotting  mean smoothness  vs  mean compactness
Plotting  mean smoothness  vs  mean concavity
Plotting  mean smoothness  vs  mean concave points
Plotting  mean smoothness  vs  mean symmetry
Plotting  mean smoothness  vs  mean fractal dimension
Plotting  mean smoothness  vs  radius error
Plotting  mean smoothness  vs  texture error
Plotting  mean smoothness  vs  perimeter error
Plotting  mean smoothness  vs  area error
Plotting  mean smoothness  vs  smoothness error
Plotting  mean smoothness  vs  compactness error
Plotting  mean smoothness  vs  concavity error
Plotting  mean smoothness  vs  concave points error
Plotting  mean smoothness  vs  symmetry error
Plotting  mean smoothness  vs  fractal dimension error
Plotting  mean smoothness  vs  worst radius
Plotting  mean smoothness  vs  worst texture
Plotting  mean smoothness  vs  worst perimeter
Plotting  mean smoothness  vs  worst area
Plotting  mean smoothness  vs  worst smoothness
Plotting  mean smoothness  vs  worst compactness
Plotting  mean smoothness  vs  worst concavity
Plotting  mean smoothness  vs  worst concave points
Plotting  mean smoothness  vs  worst symmetry
Plotting  mean smoothness  vs  worst fractal dimension
Plotting  mean concavity  vs  mean texture
Plotting  mean concavity  vs  mean area
Plotting  mean concavity  vs  mean compactness
Plotting  mean concavity  vs  mean concave points
Plotting  mean concavity  vs  mean symmetry
Plotting  mean concavity  vs  mean fractal dimension
Plotting  mean concavity  vs  radius error
Plotting  mean concavity  vs  texture error
Plotting  mean concavity  vs  perimeter error
Plotting  mean concavity  vs  area error
Plotting  mean concavity  vs  smoothness error
Plotting  mean concavity  vs  compactness error
Plotting  mean concavity  vs  concavity error
Plotting  mean concavity  vs  concave points error
Plotting  mean concavity  vs  symmetry error
Plotting  mean concavity  vs  fractal dimension error
Plotting  mean concavity  vs  worst radius
Plotting  mean concavity  vs  worst texture
Plotting  mean concavity  vs  worst perimeter
Plotting  mean concavity  vs  worst area
Plotting  mean concavity  vs  worst smoothness
Plotting  mean concavity  vs  worst compactness
Plotting  mean concavity  vs  worst concavity
Plotting  mean concavity  vs  worst concave points
Plotting  mean concavity  vs  worst symmetry
Plotting  mean concavity  vs  worst fractal dimension
Plotting  mean symmetry  vs  mean texture
Plotting  mean symmetry  vs  mean area
Plotting  mean symmetry  vs  mean compactness
Plotting  mean symmetry  vs  mean concave points
Plotting  mean symmetry  vs  mean fractal dimension
Plotting  mean symmetry  vs  radius error
Plotting  mean symmetry  vs  texture error
Plotting  mean symmetry  vs  perimeter error
Plotting  mean symmetry  vs  area error
Plotting  mean symmetry  vs  smoothness error
Plotting  mean symmetry  vs  compactness error
Plotting  mean symmetry  vs  concavity error
Plotting  mean symmetry  vs  concave points error
Plotting  mean symmetry  vs  symmetry error
Plotting  mean symmetry  vs  fractal dimension error
Plotting  mean symmetry  vs  worst radius
Plotting  mean symmetry  vs  worst texture
Plotting  mean symmetry  vs  worst perimeter
Plotting  mean symmetry  vs  worst area
Plotting  mean symmetry  vs  worst smoothness
Plotting  mean symmetry  vs  worst compactness
Plotting  mean symmetry  vs  worst concavity
Plotting  mean symmetry  vs  worst concave points
Plotting  mean symmetry  vs  worst symmetry
Plotting  mean symmetry  vs  worst fractal dimension
Plotting  radius error  vs  mean texture
Plotting  radius error  vs  mean area
Plotting  radius error  vs  mean compactness
Plotting  radius error  vs  mean concave points
Plotting  radius error  vs  mean fractal dimension
Plotting  radius error  vs  texture error
Plotting  radius error  vs  perimeter error
Plotting  radius error  vs  area error
Plotting  radius error  vs  smoothness error
Plotting  radius error  vs  compactness error
Plotting  radius error  vs  concavity error
Plotting  radius error  vs  concave points error
Plotting  radius error  vs  symmetry error
Plotting  radius error  vs  fractal dimension error
Plotting  radius error  vs  worst radius
Plotting  radius error  vs  worst texture
Plotting  radius error  vs  worst perimeter
Plotting  radius error  vs  worst area
Plotting  radius error  vs  worst smoothness
Plotting  radius error  vs  worst compactness
Plotting  radius error  vs  worst concavity
Plotting  radius error  vs  worst concave points
Plotting  radius error  vs  worst symmetry
Plotting  radius error  vs  worst fractal dimension
Plotting  perimeter error  vs  mean texture
Plotting  perimeter error  vs  mean area
Plotting  perimeter error  vs  mean compactness
Plotting  perimeter error  vs  mean concave points
Plotting  perimeter error  vs  mean fractal dimension
Plotting  perimeter error  vs  texture error
Plotting  perimeter error  vs  area error
Plotting  perimeter error  vs  smoothness error
Plotting  perimeter error  vs  compactness error
Plotting  perimeter error  vs  concavity error
Plotting  perimeter error  vs  concave points error
Plotting  perimeter error  vs  symmetry error
Plotting  perimeter error  vs  fractal dimension error
Plotting  perimeter error  vs  worst radius
Plotting  perimeter error  vs  worst texture
Plotting  perimeter error  vs  worst perimeter
Plotting  perimeter error  vs  worst area
Plotting  perimeter error  vs  worst smoothness
Plotting  perimeter error  vs  worst compactness
Plotting  perimeter error  vs  worst concavity
Plotting  perimeter error  vs  worst concave points
Plotting  perimeter error  vs  worst symmetry
Plotting  perimeter error  vs  worst fractal dimension
Plotting  smoothness error  vs  mean texture
Plotting  smoothness error  vs  mean area
Plotting  smoothness error  vs  mean compactness
Plotting  smoothness error  vs  mean concave points
Plotting  smoothness error  vs  mean fractal dimension
Plotting  smoothness error  vs  texture error
Plotting  smoothness error  vs  area error
Plotting  smoothness error  vs  compactness error
Plotting  smoothness error  vs  concavity error
Plotting  smoothness error  vs  concave points error
Plotting  smoothness error  vs  symmetry error
Plotting  smoothness error  vs  fractal dimension error
Plotting  smoothness error  vs  worst radius
Plotting  smoothness error  vs  worst texture
Plotting  smoothness error  vs  worst perimeter
Plotting  smoothness error  vs  worst area
Plotting  smoothness error  vs  worst smoothness
Plotting  smoothness error  vs  worst compactness
Plotting  smoothness error  vs  worst concavity
Plotting  smoothness error  vs  worst concave points
Plotting  smoothness error  vs  worst symmetry
Plotting  smoothness error  vs  worst fractal dimension
Plotting  concavity error  vs  mean texture
Plotting  concavity error  vs  mean area
Plotting  concavity error  vs  mean compactness
Plotting  concavity error  vs  mean concave points
Plotting  concavity error  vs  mean fractal dimension
Plotting  concavity error  vs  texture error
Plotting  concavity error  vs  area error
Plotting  concavity error  vs  compactness error
Plotting  concavity error  vs  concave points error
Plotting  concavity error  vs  symmetry error
Plotting  concavity error  vs  fractal dimension error
Plotting  concavity error  vs  worst radius
Plotting  concavity error  vs  worst texture
Plotting  concavity error  vs  worst perimeter
Plotting  concavity error  vs  worst area
Plotting  concavity error  vs  worst smoothness
Plotting  concavity error  vs  worst compactness
Plotting  concavity error  vs  worst concavity
Plotting  concavity error  vs  worst concave points
Plotting  concavity error  vs  worst symmetry
Plotting  concavity error  vs  worst fractal dimension
Plotting  symmetry error  vs  mean texture
Plotting  symmetry error  vs  mean area
Plotting  symmetry error  vs  mean compactness
Plotting  symmetry error  vs  mean concave points
Plotting  symmetry error  vs  mean fractal dimension
Plotting  symmetry error  vs  texture error
Plotting  symmetry error  vs  area error
Plotting  symmetry error  vs  compactness error
Plotting  symmetry error  vs  concave points error
Plotting  symmetry error  vs  fractal dimension error
Plotting  symmetry error  vs  worst radius
Plotting  symmetry error  vs  worst texture
Plotting  symmetry error  vs  worst perimeter
Plotting  symmetry error  vs  worst area
Plotting  symmetry error  vs  worst smoothness
Plotting  symmetry error  vs  worst compactness
Plotting  symmetry error  vs  worst concavity
Plotting  symmetry error  vs  worst concave points
Plotting  symmetry error  vs  worst symmetry
Plotting  symmetry error  vs  worst fractal dimension
Plotting  worst radius  vs  mean texture
Plotting  worst radius  vs  mean area
Plotting  worst radius  vs  mean compactness
Plotting  worst radius  vs  mean concave points
Plotting  worst radius  vs  mean fractal dimension
Plotting  worst radius  vs  texture error
Plotting  worst radius  vs  area error
Plotting  worst radius  vs  compactness error
Plotting  worst radius  vs  concave points error
Plotting  worst radius  vs  fractal dimension error
Plotting  worst radius  vs  worst texture
Plotting  worst radius  vs  worst perimeter
Plotting  worst radius  vs  worst area
Plotting  worst radius  vs  worst smoothness
Plotting  worst radius  vs  worst compactness
Plotting  worst radius  vs  worst concavity
Plotting  worst radius  vs  worst concave points
Plotting  worst radius  vs  worst symmetry
Plotting  worst radius  vs  worst fractal dimension
Plotting  worst perimeter  vs  mean texture
Plotting  worst perimeter  vs  mean area
Plotting  worst perimeter  vs  mean compactness
Plotting  worst perimeter  vs  mean concave points
Plotting  worst perimeter  vs  mean fractal dimension
Plotting  worst perimeter  vs  texture error
Plotting  worst perimeter  vs  area error
Plotting  worst perimeter  vs  compactness error
Plotting  worst perimeter  vs  concave points error
Plotting  worst perimeter  vs  fractal dimension error
Plotting  worst perimeter  vs  worst texture
Plotting  worst perimeter  vs  worst area
Plotting  worst perimeter  vs  worst smoothness
Plotting  worst perimeter  vs  worst compactness
Plotting  worst perimeter  vs  worst concavity
Plotting  worst perimeter  vs  worst concave points
Plotting  worst perimeter  vs  worst symmetry
Plotting  worst perimeter  vs  worst fractal dimension
Plotting  worst smoothness  vs  mean texture
Plotting  worst smoothness  vs  mean area
Plotting  worst smoothness  vs  mean compactness
Plotting  worst smoothness  vs  mean concave points
Plotting  worst smoothness  vs  mean fractal dimension
Plotting  worst smoothness  vs  texture error
Plotting  worst smoothness  vs  area error
Plotting  worst smoothness  vs  compactness error
Plotting  worst smoothness  vs  concave points error
Plotting  worst smoothness  vs  fractal dimension error
Plotting  worst smoothness  vs  worst texture
Plotting  worst smoothness  vs  worst area
Plotting  worst smoothness  vs  worst compactness
Plotting  worst smoothness  vs  worst concavity
Plotting  worst smoothness  vs  worst concave points
Plotting  worst smoothness  vs  worst symmetry
Plotting  worst smoothness  vs  worst fractal dimension
Plotting  worst concavity  vs  mean texture
Plotting  worst concavity  vs  mean area
Plotting  worst concavity  vs  mean compactness
Plotting  worst concavity  vs  mean concave points
Plotting  worst concavity  vs  mean fractal dimension
Plotting  worst concavity  vs  texture error
Plotting  worst concavity  vs  area error
Plotting  worst concavity  vs  compactness error
Plotting  worst concavity  vs  concave points error
Plotting  worst concavity  vs  fractal dimension error
Plotting  worst concavity  vs  worst texture
Plotting  worst concavity  vs  worst area
Plotting  worst concavity  vs  worst compactness
Plotting  worst concavity  vs  worst concave points
Plotting  worst concavity  vs  worst symmetry
Plotting  worst concavity  vs  worst fractal dimension
Plotting  worst symmetry  vs  mean texture
Plotting  worst symmetry  vs  mean area
Plotting  worst symmetry  vs  mean compactness
Plotting  worst symmetry  vs  mean concave points
Plotting  worst symmetry  vs  mean fractal dimension
Plotting  worst symmetry  vs  texture error
Plotting  worst symmetry  vs  area error
Plotting  worst symmetry  vs  compactness error
Plotting  worst symmetry  vs  concave points error
Plotting  worst symmetry  vs  fractal dimension error
Plotting  worst symmetry  vs  worst texture
Plotting  worst symmetry  vs  worst area
Plotting  worst symmetry  vs  worst compactness
Plotting  worst symmetry  vs  worst concave points
Plotting  worst symmetry  vs  worst fractal dimension
Número de gráficos:  330

In [10]:

from sklearn.decomposition import PCA

pca = PCA()
#pca.fit(X)
#pca.transform(X)
pcs = pca.fit_transform(X)
print(pcs.shape)
print(X.shape)

from sklearn.decomposition import PCA pca = PCA() #pca.fit(X) #pca.transform(X) pcs = pca.fit_transform(X) print(pcs.shape) print(X.shape)

(569, 30)
(569, 30)

In [11]:

plt.figure(figsize=(10,6))
plt.scatter(pcs[:,0], pcs[:,1], c = color_map)
plt.title('Gráfico 2 componentes principales')
plt.xlabel('PC1')
plt.ylabel('PC2')
plt.show()

plt.figure(figsize=(10,6)) plt.scatter(pcs[:,0], pcs[:,1], c = color_map) plt.title('Gráfico 2 componentes principales') plt.xlabel('PC1') plt.ylabel('PC2') plt.show()

Usando PCA para entrenamiento¶

In [12]:

from sklearn.decomposition import PCA
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LogisticRegression


X = cancer_data.data
y = cancer_data.target

X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42, test_size=0.2, stratify=y)

# Instanciar Escalador Estándar
scaler = StandardScaler()
# Ajustar y transformar datos
X_train = scaler.fit_transform(X_train)
X_test = scaler.transform(X_test)

from sklearn.decomposition import PCA from sklearn.model_selection import train_test_split from sklearn.linear_model import LogisticRegression X = cancer_data.data y = cancer_data.target X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42, test_size=0.2, stratify=y) # Instanciar Escalador Estándar scaler = StandardScaler() # Ajustar y transformar datos X_train = scaler.fit_transform(X_train) X_test = scaler.transform(X_test)

In [13]:

pca = PCA(n_components=10) # Prueba cambiando el número de componentes!!
X_train_pca = pca.fit_transform(X_train)
X_test_pca = pca.transform(X_test)

pca = PCA(n_components=10) # Prueba cambiando el número de componentes!! X_train_pca = pca.fit_transform(X_train) X_test_pca = pca.transform(X_test)

In [14]:

%%time
# Sin PCA
logreg = LogisticRegression()
logreg.fit(X_train, y_train)

logreg.score(X_test, y_test)

%%time # Sin PCA logreg = LogisticRegression() logreg.fit(X_train, y_train) logreg.score(X_test, y_test)

CPU times: user 34.7 ms, sys: 172 ms, total: 206 ms
Wall time: 16.3 ms

Out[14]:

0.9824561403508771

In [15]:

%%time
# Con PCA
logreg_pca = LogisticRegression()
logreg_pca.fit(X_train_pca, y_train)

logreg_pca.score(X_test_pca, y_test)

%%time # Con PCA logreg_pca = LogisticRegression() logreg_pca.fit(X_train_pca, y_train) logreg_pca.score(X_test_pca, y_test)

CPU times: user 5.1 ms, sys: 602 µs, total: 5.7 ms
Wall time: 4.73 ms

Out[15]:

0.9736842105263158

Escogiendo cantidad de componentes PCA¶

Existen varios criterios para escoger los componentes más importantes

• Criterio del codo en base a la varianza (utilizar atributo explained_variance_ratio_ presente en objeto PCA)

In [16]:

pca = PCA()
X_train_pca = pca.fit_transform(X_train)

plt.figure(figsize=(10,6))
plt.plot(pca.explained_variance_ratio_,'bo-')
plt.show()

pca = PCA() X_train_pca = pca.fit_transform(X_train) plt.figure(figsize=(10,6)) plt.plot(pca.explained_variance_ratio_,'bo-') plt.show()

• Porcentaje de la varianza a tomar en cuenta. Este dato se entrega en el entrenamiento.
  • Ej. Si deseamos las componentes que contienen el 95% de la varianza, entrenamos el algoritmo PCA como se ve a continuación

In [17]:

pca = PCA(n_components=0.95)
X_train_pca = pca.fit_transform(X_train)

print("El número de componentes es", pca.n_components_, "de", pca.n_features_)

pca = PCA(n_components=0.95) X_train_pca = pca.fit_transform(X_train) print("El número de componentes es", pca.n_components_, "de", pca.n_features_)

El número de componentes es 10 de 30

Ejemplo de uso PCA: eigenfaces¶

In [18]:

from sklearn.datasets import fetch_olivetti_faces

faces = fetch_olivetti_faces()
X = faces.data
y = faces.target

fig = plt.figure(figsize=(13,13))

n = 16
for i in range(1,n+1):
    ax = fig.add_subplot(4,4,i)
    ax.imshow(X[i].reshape(64,64), cmap='gray')

plt.show()
print(X.shape)

from sklearn.datasets import fetch_olivetti_faces faces = fetch_olivetti_faces() X = faces.data y = faces.target fig = plt.figure(figsize=(13,13)) n = 16 for i in range(1,n+1): ax = fig.add_subplot(4,4,i) ax.imshow(X[i].reshape(64,64), cmap='gray') plt.show() print(X.shape)

(400, 4096)

In [19]:

from sklearn.decomposition import PCA

pca = PCA()
pcs = pca.fit_transform(X)

pca.components_.shape

from sklearn.decomposition import PCA pca = PCA() pcs = pca.fit_transform(X) pca.components_.shape

Out[19]:

(400, 4096)

In [20]:

pca.singular_values_

pca.singular_values_

Out[20]:

array([8.67019730e+01, 6.64652557e+01, 5.01551704e+01, 3.97225189e+01,
       3.37573624e+01, 3.15687275e+01, 2.76786003e+01, 2.53545341e+01,
       2.48624077e+01, 2.29751530e+01, 2.24406242e+01, 2.12985268e+01,
       1.98386669e+01, 1.90296707e+01, 1.83174915e+01, 1.75683746e+01,
       1.70332050e+01, 1.60456028e+01, 1.54267321e+01, 1.53560791e+01,
       1.48501873e+01, 1.39293432e+01, 1.35770054e+01, 1.34108419e+01,
       1.31309624e+01, 1.29574947e+01, 1.27358618e+01, 1.25111065e+01,
       1.20198154e+01, 1.18014135e+01, 1.12651854e+01, 1.10127869e+01,
       1.06893015e+01, 1.02766113e+01, 1.00567503e+01, 9.98840523e+00,
       9.81475353e+00, 9.70944691e+00, 9.43751049e+00, 9.30046749e+00,
       9.05566788e+00, 8.95432854e+00, 8.78629017e+00, 8.70131207e+00,
       8.53743458e+00, 8.45436287e+00, 8.37684822e+00, 8.34203815e+00,
       8.12110233e+00, 8.04420757e+00, 7.88286734e+00, 7.77384901e+00,
       7.64300728e+00, 7.51582861e+00, 7.48782730e+00, 7.37899303e+00,
       7.29514360e+00, 7.19894505e+00, 7.14871931e+00, 7.07121754e+00,
       7.00469780e+00, 6.93232012e+00, 6.88031626e+00, 6.82861328e+00,
       6.70961332e+00, 6.66213179e+00, 6.57492971e+00, 6.50328207e+00,
       6.42863846e+00, 6.37451029e+00, 6.34244680e+00, 6.31260109e+00,
       6.25152540e+00, 6.18892288e+00, 6.10028791e+00, 6.02212143e+00,
       6.00382137e+00, 5.89770222e+00, 5.88435698e+00, 5.85578203e+00,
       5.79922915e+00, 5.74895144e+00, 5.66556644e+00, 5.58420229e+00,
       5.54736567e+00, 5.51564598e+00, 5.49353647e+00, 5.42735195e+00,
       5.36528921e+00, 5.35552740e+00, 5.30220890e+00, 5.27387190e+00,
       5.25750446e+00, 5.22422743e+00, 5.10435677e+00, 5.04701757e+00,
       5.01673603e+00, 5.00707054e+00, 4.98338270e+00, 4.93973160e+00,
       4.89162683e+00, 4.87898350e+00, 4.83393717e+00, 4.81472349e+00,
       4.76173401e+00, 4.73932409e+00, 4.70194387e+00, 4.65496778e+00,
       4.61132574e+00, 4.59201193e+00, 4.55551958e+00, 4.54440308e+00,
       4.49239588e+00, 4.46295786e+00, 4.43636084e+00, 4.42737246e+00,
       4.39764738e+00, 4.32589483e+00, 4.31439400e+00, 4.27803040e+00,
       4.25079823e+00, 4.21890879e+00, 4.18245316e+00, 4.15838623e+00,
       4.14846373e+00, 4.13530159e+00, 4.12223387e+00, 4.08655691e+00,
       4.06819963e+00, 4.04153681e+00, 4.01971722e+00, 3.96746087e+00,
       3.94706655e+00, 3.91783357e+00, 3.89643955e+00, 3.88215613e+00,
       3.86362410e+00, 3.83839226e+00, 3.82244968e+00, 3.79968786e+00,
       3.75180507e+00, 3.74326634e+00, 3.72621131e+00, 3.69316649e+00,
       3.66814423e+00, 3.66080093e+00, 3.64558458e+00, 3.63340139e+00,
       3.59850621e+00, 3.58630037e+00, 3.57101560e+00, 3.54475188e+00,
       3.53729439e+00, 3.51334643e+00, 3.50319576e+00, 3.49361658e+00,
       3.46752691e+00, 3.43627882e+00, 3.42637277e+00, 3.41486120e+00,
       3.39643526e+00, 3.37961507e+00, 3.36745453e+00, 3.34750700e+00,
       3.32401586e+00, 3.30961466e+00, 3.29122925e+00, 3.26569581e+00,
       3.25932407e+00, 3.23354721e+00, 3.22916937e+00, 3.21766758e+00,
       3.18845677e+00, 3.16987205e+00, 3.14393115e+00, 3.13798332e+00,
       3.13632321e+00, 3.10858941e+00, 3.09750390e+00, 3.08093834e+00,
       3.05235863e+00, 3.03736448e+00, 3.01557088e+00, 2.99736953e+00,
       2.97718096e+00, 2.96695542e+00, 2.93944931e+00, 2.93521857e+00,
       2.91714478e+00, 2.91031051e+00, 2.89646721e+00, 2.88030362e+00,
       2.86871934e+00, 2.85353565e+00, 2.84549403e+00, 2.82542944e+00,
       2.81264138e+00, 2.80306578e+00, 2.78921080e+00, 2.75221419e+00,
       2.74593949e+00, 2.72394443e+00, 2.72214007e+00, 2.71539831e+00,
       2.70571685e+00, 2.68297577e+00, 2.67742538e+00, 2.67121172e+00,
       2.65917253e+00, 2.63410902e+00, 2.62550092e+00, 2.61427116e+00,
       2.59991026e+00, 2.57830143e+00, 2.57135749e+00, 2.56946087e+00,
       2.53385353e+00, 2.52855587e+00, 2.50926447e+00, 2.50185418e+00,
       2.48441792e+00, 2.47901320e+00, 2.47376800e+00, 2.45884299e+00,
       2.44685650e+00, 2.44085217e+00, 2.42005348e+00, 2.41766381e+00,
       2.40895438e+00, 2.39749312e+00, 2.39310122e+00, 2.37524271e+00,
       2.35588694e+00, 2.34345913e+00, 2.32700181e+00, 2.31737208e+00,
       2.30046058e+00, 2.29415107e+00, 2.28666425e+00, 2.28088403e+00,
       2.25738430e+00, 2.24987793e+00, 2.24142313e+00, 2.22998047e+00,
       2.22279263e+00, 2.21069574e+00, 2.19862056e+00, 2.19633174e+00,
       2.18271542e+00, 2.16603637e+00, 2.16189456e+00, 2.14149523e+00,
       2.13907576e+00, 2.12251067e+00, 2.10614324e+00, 2.10067153e+00,
       2.09049845e+00, 2.08798003e+00, 2.08485126e+00, 2.07021046e+00,
       2.05914712e+00, 2.05065632e+00, 2.04303241e+00, 2.02948570e+00,
       2.01394176e+00, 2.00638318e+00, 2.00006008e+00, 1.99645925e+00,
       1.98778737e+00, 1.97274339e+00, 1.96629345e+00, 1.95498490e+00,
       1.95113802e+00, 1.94224048e+00, 1.93135357e+00, 1.92090797e+00,
       1.91690063e+00, 1.90727794e+00, 1.89598942e+00, 1.88704824e+00,
       1.88123226e+00, 1.87268841e+00, 1.86351442e+00, 1.85769570e+00,
       1.85189319e+00, 1.84708476e+00, 1.83549905e+00, 1.83239698e+00,
       1.81746566e+00, 1.80466330e+00, 1.79198551e+00, 1.78123844e+00,
       1.76884556e+00, 1.75707817e+00, 1.75288594e+00, 1.74518907e+00,
       1.73888075e+00, 1.73014629e+00, 1.72320902e+00, 1.71455085e+00,
       1.71072924e+00, 1.69756186e+00, 1.69096172e+00, 1.68947208e+00,
       1.68282592e+00, 1.65408599e+00, 1.65107608e+00, 1.64000714e+00,
       1.63345230e+00, 1.62733793e+00, 1.62501168e+00, 1.61390746e+00,
       1.61244512e+00, 1.60437238e+00, 1.58399594e+00, 1.58141637e+00,
       1.57921565e+00, 1.56690443e+00, 1.56132340e+00, 1.54932296e+00,
       1.54774010e+00, 1.54119098e+00, 1.52550340e+00, 1.51659071e+00,
       1.50771141e+00, 1.49963534e+00, 1.49366891e+00, 1.48807275e+00,
       1.48013783e+00, 1.47570050e+00, 1.47361946e+00, 1.46197701e+00,
       1.45815635e+00, 1.44604146e+00, 1.43327284e+00, 1.43002021e+00,
       1.42324698e+00, 1.41398966e+00, 1.40300941e+00, 1.39303148e+00,
       1.38711798e+00, 1.38159633e+00, 1.37085938e+00, 1.35424531e+00,
       1.34968066e+00, 1.34868908e+00, 1.33929455e+00, 1.33017850e+00,
       1.31506407e+00, 1.31415212e+00, 1.29742253e+00, 1.29378426e+00,
       1.27884734e+00, 1.27379715e+00, 1.26695335e+00, 1.25753713e+00,
       1.24858522e+00, 1.24823749e+00, 1.23656499e+00, 1.22576010e+00,
       1.22270632e+00, 1.21047401e+00, 1.20913112e+00, 1.20086586e+00,
       1.18829727e+00, 1.17658353e+00, 1.16693616e+00, 1.15184510e+00,
       1.14749789e+00, 1.14276719e+00, 1.13625574e+00, 1.12693357e+00,
       1.11847591e+00, 1.10988426e+00, 1.10522521e+00, 1.09566057e+00,
       1.09356129e+00, 1.07322633e+00, 1.06727886e+00, 1.05904663e+00,
       1.03996456e+00, 1.03270960e+00, 1.02170205e+00, 1.01863468e+00,
       1.00697589e+00, 1.00185668e+00, 9.90437388e-01, 9.79656398e-01,
       9.62462962e-01, 9.40755069e-01, 9.24248576e-01, 9.06024814e-01,
       8.86753857e-01, 8.70458901e-01, 8.34254324e-01, 8.28883350e-01,
       8.22203100e-01, 7.95056880e-01, 7.19473183e-01, 1.97418791e-04],
      dtype=float32)

In [21]:

fig = plt.figure(figsize=(13,13))

n = 16
for i in range(0,n):
    ax = fig.add_subplot(4,4,i+1)
    ax.imshow(pca.components_[i].reshape(64,64), cmap='gray')

plt.show()

fig = plt.figure(figsize=(13,13)) n = 16 for i in range(0,n): ax = fig.add_subplot(4,4,i+1) ax.imshow(pca.components_[i].reshape(64,64), cmap='gray') plt.show()

Linear Discriminant Analysis (LDA)¶

• Es un algoritmo de clasificación, que aprende los ejes más discriminativos entre clases.
• La proyección resultante mantiene las clases tan separadas como sea posible.

In [22]:

import matplotlib.pyplot as plt
from sklearn.datasets import load_breast_cancer
import pandas as pd

cancer_data = load_breast_cancer(as_frame=True) # Para obtener datos como dataframe
print(cancer_data.target_names) # 0 Maligno, 1 benigno

import matplotlib.pyplot as plt from sklearn.datasets import load_breast_cancer import pandas as pd cancer_data = load_breast_cancer(as_frame=True) # Para obtener datos como dataframe print(cancer_data.target_names) # 0 Maligno, 1 benigno

['malignant' 'benign']

In [23]:

from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
import numpy as np

X = cancer_data.data
y = cancer_data.target

X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42, test_size=0.2, stratify=y)

# Instanciar Escalador Estándar
scaler = StandardScaler()
# Ajustar y transformar datos
X_train = scaler.fit_transform(X_train)
X_test = scaler.transform(X_test)

from sklearn.discriminant_analysis import LinearDiscriminantAnalysis from sklearn.model_selection import train_test_split from sklearn.preprocessing import StandardScaler import numpy as np X = cancer_data.data y = cancer_data.target X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42, test_size=0.2, stratify=y) # Instanciar Escalador Estándar scaler = StandardScaler() # Ajustar y transformar datos X_train = scaler.fit_transform(X_train) X_test = scaler.transform(X_test)

In [24]:

lda = LinearDiscriminantAnalysis()
X_train_lda = lda.fit_transform(X_train, y_train)
lda.score(X_test, y_test)

lda = LinearDiscriminantAnalysis() X_train_lda = lda.fit_transform(X_train, y_train) lda.score(X_test, y_test)

Out[24]:

0.956140350877193

In [25]:

# Proyectando
colors = {0:'red', 1:'green'}
color_map = y_train.map(colors)

plt.figure(figsize=(10,6))
plt.scatter(X_train_lda,np.zeros_like(X_train_lda), c=color_map)
plt.show()

# Proyectando colors = {0:'red', 1:'green'} color_map = y_train.map(colors) plt.figure(figsize=(10,6)) plt.scatter(X_train_lda,np.zeros_like(X_train_lda), c=color_map) plt.show()

Actividad 9¶

¡Hora de poner en práctica todo lo aprendido hasta ahora!

• Estudie el dataset California Housing presente en los dataset de Scikit-Learn (enlace aquí)
• Cree un Pipeline completo que permita predecir el precio de una casa.

In [ ]:

from IPython.core.display import HTML
HTML("""
<style>
.output_png {
    display: table-cell;
    text-align: center;
    vertical-align: middle;
}
</style>
""")
#codigo extra, para que imagenes de matplotlib
#estén centradas en las diapositivas, ejecutar antes de lanzar los ejemplos.

from IPython.core.display import HTML HTML(""" """) #codigo extra, para que imagenes de matplotlib #estén centradas en las diapositivas, ejecutar antes de lanzar los ejemplos.